MATH 161
EXAM 1
1. (48 pt) Evaluate the following:
a) b)
c)
d) e)
f)
2. (10 pt) Find the area between the curves and
.
3. (10 pt) Find the volume obtained by revolving the region bounded by and
about the line y=1.
4. (10 pt) Show that the volume of a right circular cylinder of base radius R and height h has volume given by the formula: V=(1/3)p R2h.
5. (12 pt) Consider the function defined by if
and
if
. Find the average value of
on the interval [-p
,1]. Is there a value (say c) in [-p
,1] such that
? Does this contradict the mean value theorem for integrals?
6. (10 pt) Let be a differentiable function such that
and
. Find
7. EXTRA CREDIT (5 pt) Let . Find